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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is  <a href="lfuzzy_0.html#V2" title="LFUZZY_0:attr.2">interval</a>  implies ( <font color="Maroon" title="c1">R</font> is  <a href="lfuzzy_0.html#V1" title="LFUZZY_0:attr.1">real</a>  &amp;  not <font color="Maroon" title="c1">R</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:3_1_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c1">R</font> is  <a href="lfuzzy_0.html#V1" title="LFUZZY_0:attr.1">real</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lfuzzy_0.html#D2" target="_self" title="LFUZZY_0:def.2">LFUZZY_0:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   holds <br/>(  not <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b</font> or  not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> ) or ( <font color="Maroon" title="c1">R</font> is  <a href="lfuzzy_0.html#V1" title="LFUZZY_0:attr.1">real</a>  &amp;  not <font color="Maroon" title="c1">R</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><a NAME="E3:3_1_1"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is  <a href="lfuzzy_0.html#V1" title="LFUZZY_0:attr.1">real</a>  &amp;  not <font color="Maroon" title="c1">R</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:3_1_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="lfuzzy_0.html#V1" title="LFUZZY_0:attr.1">real</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c1">R</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> </span><br/>

<span class="kw">thus </span><a NAME="E5:3_1_1"/>
 not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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